A (fuzzy) definition

Bioinformatics studies the information content and data flow in a biological system or process. It provides the link between the observations (data), the understanding of how a system works (information), and the subsequent application of these principles (knowledge).

Research areas (by "dimensionality")

1D,2D: Gene identification in Genome, sequence analysis (similarity, evolutionary distances, etc.), expression dynamics, etc.

3D: Structure similarities, dynamic changes, protein folding, structure-function relationships, etc.

nD: Protein ensembles in a cell, interaction networks, expression pathways, etc.